Scaled consensus for coupled harmonic oscillators via sampled position data

This study considers the scaled consensus problem of coupled harmonic oscillators with a directed network topology. A distributed control protocol with input delay and intermittent sampled position information only is proposed. To achieve consensus, a necessary and sufficient condition depending on communication width, input delay and sampling period is derived. Furthermore, to save energy and improve the efficiency of communication among the agents and their neighbours, the authors extend their argument to investigate an impulsive control protocol. Different from intermittent control, the scaled consensus under the impulsive control cannot be achieved if there is no input delay. Numerical simulations illustrate that appropriately chosen control gains can verify the theoretical results.